Complementary Mean-square Analysis of CNLMS Algorithm using Pseudo-energy-conservation Method

This study develops a pseudo-energy-conservation relation to analyze the complementary mean-square performance of a complex-valued normalized least mean-square (CNLMS) algorithm. Based on this relation, we derive a recursion describing the transient complementary mean-square deviation (CMSD) behavior of the CNLMS. Closed-form expressions to predict the steady-state CMSD and complementary excess mean-square error conjugate (CEMSEc) are obtained. Because this method inherits the advantages of the energy-conservation method, our results do not restrict the distribution of input signals. Numerical simulations validate our theoretical analysis results.